It's been too long since I have done differential equations and I am not sure the best tools to solve this problem. I am starting with a basic kinematic equation for the balance of forces. P\v - ((A*Cw*Rho*v^2)/2 + m*g*Crl + m*g*slope) = m*a P: power x: position v: velocity, x' a: acceleration x" (A*Cw*Rho*v^2)/2 : air resistance m*g*Crl : rolling resistance m*g*slope : potential energy (elevation)
I am modifying the above equation so that air velocity and slope are dependant on location x. Vair = v + f(x) where f(x) is the weather component and a function of location x. Same goes for slope, slope = g(x) Power is a function I what to optimize/find to minimize time but at this time just simulate. maybe something like: P = 2500/(v+1) I will have restriction on P but not interested in that now. The "course" I what to simulate therefore defines slope and wind speed. and is of a fixed distance. I have played with some of the simple scipy.integrate.odeint examples. I get that I need to define a system of equations but am not really sure the rules for doing so. A little help would be greatly appreciated. Vincent Davis 720-301-3003
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